河道中典型边界上湍流运动的数值模拟研究
摘要
天然河道与水利水电与航运工程中的实际流动均属复杂边界下的湍流运动。例如：河道内沙波河床上的流动、粗糙床面上的流动、绕洲滩的流动、植被覆盖河床上的流动等等,其中沙波河床上的流动和粗糙床面尤其是粗糙度变化河床上的流动两种边界存在十分广泛。其显著改变了近底水流运动结构,进而对河道的泄流能力、推移质输沙率变化、悬移质输移以及床面形态的调整都起着重要的作用。本文选取沙波河床和粗糙度变化河床两种典型边界,对其水流运动特性进行了研究,以进一步加深典型边界上的流动的认识。为水利水电、航运等工程的规划、设计和建设提供可靠的技术基础。本文主要结论如下：
(1)建立了河道内典型边界上的水流运动数学模型。采用雷诺应力模式来封闭流动控制方程。在数学模型中采用统一的壁函数来反映组成河床边界的沙粒对水流运动的影响。在沙波上水流运动计算中,选用相对粗糙高度、沙波陡度与相对波高作为参数来描述沙波的几何特征；在粗糙度变化床面上流动计算中,采用不同的粗糙高度来描述床面粗糙度变化。验证计算成果表明：沙波河床上与粗糙度变化河床上水流时均流速、时均切应力的已有的实测值和计算值均基本吻合,表明已建立的模型能够反映沙波河床以及粗糙度变化河床上水流运动的主要特征。
(2)对沙波阻力与沙粒阻力进行了系统的研究。沙波河床上沙粒阻力为表面阻力,其阻力系数主要与雷诺数、相对粗糙度以及沙波陡度有关,且其值要高于相同条件下平坦床面上的沙粒阻力系数。沙波河床上的沙波阻力属于形体阻力,其阻力系数主要取决于沙波相对高度与沙波陡度。在沙波相对波高相同的条件下,沙波陡度越大,沙波的阻力系数越大。在沙波上水流运动的计算中,本文首次引入壁函数来分析沙波陡度对沙粒阻力的影响。当沙波陡度小于某一值时,河床阻力以沙粒阻力为主；当沙波陡度大于某一值时,河床阻力以沙波阻力为主。且沙波陡度越大,相应的沙粒阻力系数也越大。
(3)对沙波上的水流湍动扩散系数与泥沙扩散系数进行了比较。在平坦床面上,泥沙扩散系数与水流湍动扩散系数沿垂向分布基本一致。而在沙波河床上两者则有所不同,泥沙扩散系数出现最大值的垂向位置要高于水流湍动扩散系数出现最大值的垂向位置；但在远离壁面的范围内,泥沙扩散系数与水流湍动扩散系数基本一致。
(4)对床面粗糙度单一变化条件下水流运动特性进行了系统研究。粗糙度变化后,内边界层的发展、床面切应力和流速的调整与来流的雷诺数、粗糙度变化形式有关。研究成果表明：内边界层向下游发展,1)随着纵向距离的增加,内边界层厚度也逐渐增加；2)在不同来流雷诺数下,内边界层发展趋基本相同。但其沿程发展有随着雷诺数的增加而逐渐变缓的趋势；3)相比于床面由水力光滑突变到水力粗糙时,床面由水力粗糙突变到水力光滑内边界层的发展更为迅速。粗糙度突变以后,床面切应力的变化主要表现为,1)在粗糙度突变点下游,床面切应力出现突变,通过一段距离之后,达到新的平衡值；2)随着来流雷诺数的增加,床面切应力的突变值也同时增大,其恢复长度相应减小。3)相比于床面由水力粗糙突变到水力光滑时,床面由水力光滑突变到水力粗糙床面切应力的突变的更为显著,而其恢复长度要小于后者；粗糙度变化后,流速变化主要变现为：1)粗糙度突变后的流速变化向下游沿纵向距离的增加逐渐趋于平衡；2)受内边界层生长的影响,外区流速略有增加；3)床面由水力粗糙变化到水力光滑时,近底流速增加,床面由水力光滑变化到水力粗糙时,近底流速减小,前者流速变化值沿纵向更快地趋于平衡。
(5)对床面粗糙度交替变化条件下水流运动特性进行了较为系统的研究。由于床面粗糙度交替变化十分复杂,为了分析粗糙度交替变化后流动特性,本文选取了粗糙度变化区域长度和粗糙度变化形式两种影响因素。当床面粗糙度交替变化时,内边界层的发展主要表现为：1)粗糙度变化区域长度很短时,内边界层发展较为迅速,随着粗糙度变化区域长度的增加,内边界层的发展逐渐趋近于粗糙度单一变化时的趋势；2)粗糙度再次突变,在突变点以后,内边界层出现了新的增长。床面切应力变化主要表现为：1)粗糙度变化区域长度较短时,床面切应力在该区域内不会出现突变,只有当粗糙度变化区域的长度增加到某一值时(通常小于单一粗糙度突变条件下床面切应力的恢复长度),床面切应力才能在该区域达到新的平衡值；2)而且随着粗糙区域长度的增加,床面切应力的恢复长度先增加然后减小逐渐趋于粗糙度单一变化时床面切应力的恢复长度；3)相比于床面由水力光滑到水力过渡再到水力光滑,床面由水力光滑到水力粗糙再到水力光滑的床面切应力突变值较大,而其恢复长度较短；4)相比于床面由水力光滑到水力过渡再到水力粗糙,床面由水力粗糙到水力光滑再到水力粗糙时,床面切应力的突变值较大,而两者的恢复长度基本一致。
(6)对床面粗糙度交替变化与河床高程高程调整共同作用下的水流运动进行了初步探讨。当河床发生淤积时,同时伴随有床沙组成发生细化,床面高程有所抬高；当床沙发生冲刷时,同时伴随有床沙组成发生粗化,床面高程有所降低。在床面粗糙度交替变化与河床高程调整共同作用时,水流运动受床面高程调整的影响为主。
The physical movements in the natural riverway, the hydraulic and hydro-power and shipping engineering are all turbulent flows under complex boundary. Such as: flow on the sand wave riverbed in the riverway, flow on the rough riverbed surface, flow around sand bars, and flow on the riverbed covered by vegetation, etc. in which the complex boundaries of flow on the sand wave riverbed and the flow on the rough riverbed surface especially on the riverbed with changeable roughness exist very widely. It significantly changes the structure of water flow movement near the bottom, and then plays important roles in discharge capacity of the riverway, bed-load transport salad change, suspended load transport and the adjustment of bed surface shape. This paper selects the two typical complex boundaries of sand wave riverbed and riverbed with changeable roughness, analyzes the characteristics of the water flow movement, further deepens the understanding of typical flow on the complex boundaries, and provides the reliable technical base for the planning, design and construction of hydraulic and hydro-power engineering and shipping engineering, etc. The main conclusions of this paper are as follows:
(1) Numerical model of flow movement on the complex boundary in the riverway has been established. The Reynolds stress model is adopted to close the flow control equation. In the numerical model, unified wall functions are adopted to reflect the impact of sands forming the boundary of the riverbed on the water flow movement. In the calculation of water flow movement on the sand wave, relative roughness, ripple steepness and relative wave height are chosen to reflect the geometric characteristics of sand wave. In the calculation of flow movement on the bed surface with changeable roughness, different roughnesses are adopted to describe the changes of roughness of bed surface. Validation calculation showed that the experimental values of the mean velocity on the sand wave bed and the mean shear stress are basically same to the calculated values, which means this model precisely described the major characteristics of the flow movement on sand wave bed.
(2) A systematic study was made of the ripple resistance coefficient and the sand-grain resistance coefficient. The sand-grain resistance on sand wave bed is surface resistance, whose coefficient is correlated to Reynolds, relative roughness and ripple steepness, and the coefficient is larger than the sand-grain resistance coefficient under the same conditions. Sand wave resistance on the sand wave riverbed belongs to physical resistance; ripple resistance coefficient on sand wave bed is closely correlated to relative height and steepness of ripples. Given the same wave height of ripples, the ripple resistance coefficient rises with the increment of sand wave steepness. In calculation of flow movement on the ripple, the wavy wall function was introduced to reflect the impact of sand gain roughness upon the flow. When the steepness of ripples is less than 0.07, the bed resistance is mainly in form of sand-grain resistance; if the steepness of ripples is more than 0.07, the bed resistance is mainly in form of ripple resistance. Increase in ripple steepness results in greater sand-grain resistance.
(3) A comparison was made between the turbulent diffusion coefficient and the sediment diffusion coefficient. On a flat bed, the sediment diffusion coefficient and the turbulent diffusion coefficient on vertical distribution are almost identical, while different on the sand wave bed; and the vertical position where sediment diffusion coefficient reaches the maximum is higher than that of turbulent diffusion coefficient; but when far away from the wave wall, the sediment diffusion coefficient is basically the same as the turbulent diffusion coefficient.
(4) A systematic study was made of the flow characteristics on the bed under uniform roughness, to conclude that after change in roughness, there was correlation between development in inner boundary, adjustment in bed shear stress and flow velocity to the change in inlet flow Reynolds and in roughness. The study concluded that the inner boundary developed toward the downstream.1) Gradual increase in thickness of the inner boundary was followed by increase in vertical distance; 2) For different inlet flow Reynolds, the inner boundary developed in almost the same trend, but development along the bed tended to slow down with increment in Reynolds; 3) In case of sudden bed change from the hydraulic rough zone to the hydraulic smooth zone, the inner boundary developed much more swiftly. Sudden change in roughness results in such change in the bed shear stress as that 1) in downstream of the sudden change point of the bed roughness, there was sudden change in the bed shear stress until new balance was achieved after flow for a certain distance; 2) as the increment in the inlet flow Reynolds, sudden changed value of the bed shear stress was increased, and the recovery length correspondingly reduced.3) In case of abrupt bed change from the hydraulic smooth zone to the hydraulic rough zone, there was more noticeable sudden change in the bed shear stress and shorter recovery length for the shear stress. Change in roughness was followed by such main change in flow velocity as 1) for different values of the inlet flow Reynolds, flow velocity change caused by abrupt roughness change was distributed along the vertical bed, until to achieve balance in the downstream; 2) there was slight increment in outer boundary caused by development of inner boundary; 3) In case of sudden bed change from the hydraulic rough zone to hydraulic smooth zones, there was increment in flow velocity of underneath part close to the bed (in which case the flow velocity value is more rapidly balanced vertically along the bed); otherwise when the bed abruptly changes from the hydraulic smooth zone to the hydraulic rough zone, there was decrease in flow velocity of underneath part close to the bed.
(5) A relatively systematic study was made of the flow characteristics in case of successive change in bed roughness. Since there was complex successive change in bed roughness, for the sake of analysis of the flow characteristics after successive change in bed roughness, two factors were taken into consideration, namely the roughness change zone length and the roughness change forms. In case of successive change in bed roughness, there was such change in inner boundary in such forms as 1) in case of short roughness change zone length, the inner boundary developed swiftly. Increase in the roughness change zone length caused the inner boundary to develop in the same orientation as in case of the uniform roughness change; 2) after the second sudden change point of roughness, there was new development in the inner boundary. The bed shear stress changed in such major ways as 1) in case of relatively short roughness change zone length, there was no sudden change in the bed shear stress; only when the roughness change zone length increased to a certain point (such a length is usually shorter than the recovery length of the bed shear stress in case of uniform roughness abrupt change), would the bed shear stress achieve fresh balance in the zone concerned.2) With increase in roughness change zone length, the recovery length of the bed shear stress would be lengthened first and then reduced until to reach the recovery length of the bed shear stress in case of uniform roughness abrupt change.3) Compared with bed change from the hydraulic smooth zone to the hydraulic transition zone and then to the hydraulic smooth zone again, there was larger sudden change in the bed shear stress value but shorter recovery length in case of bed change from the hydraulic smooth zone to the hydraulic rough zone and then to the hydraulic smooth zone again; In case of bed change from the hydraulic smooth zone to the hydraulic transition zone and then to the rough zone, or in case of bed change from the hydraulic rough zone to the hydraulic smooth zone and then to the rough zone again, there was relatively limited change in the bed shear stress and recovery length.
(6) Tentative analysis was made of the flow movement caused by combined action of the bed elevation change and bed roughness change. In case of coarsening bed sand, there would be corresponding decrease in bed elevation; otherwise when the bed sand is under refinery, there would be corresponding increase in bed elevation. Under combined action of the bed elevation change and bed roughness change, the flow was mainly under impact from the bed elevation change.
(1)建立了河道内典型边界上的水流运动数学模型。采用雷诺应力模式来封闭流动控制方程。在数学模型中采用统一的壁函数来反映组成河床边界的沙粒对水流运动的影响。在沙波上水流运动计算中,选用相对粗糙高度、沙波陡度与相对波高作为参数来描述沙波的几何特征；在粗糙度变化床面上流动计算中,采用不同的粗糙高度来描述床面粗糙度变化。验证计算成果表明：沙波河床上与粗糙度变化河床上水流时均流速、时均切应力的已有的实测值和计算值均基本吻合,表明已建立的模型能够反映沙波河床以及粗糙度变化河床上水流运动的主要特征。
(2)对沙波阻力与沙粒阻力进行了系统的研究。沙波河床上沙粒阻力为表面阻力,其阻力系数主要与雷诺数、相对粗糙度以及沙波陡度有关,且其值要高于相同条件下平坦床面上的沙粒阻力系数。沙波河床上的沙波阻力属于形体阻力,其阻力系数主要取决于沙波相对高度与沙波陡度。在沙波相对波高相同的条件下,沙波陡度越大,沙波的阻力系数越大。在沙波上水流运动的计算中,本文首次引入壁函数来分析沙波陡度对沙粒阻力的影响。当沙波陡度小于某一值时,河床阻力以沙粒阻力为主；当沙波陡度大于某一值时,河床阻力以沙波阻力为主。且沙波陡度越大,相应的沙粒阻力系数也越大。
(3)对沙波上的水流湍动扩散系数与泥沙扩散系数进行了比较。在平坦床面上,泥沙扩散系数与水流湍动扩散系数沿垂向分布基本一致。而在沙波河床上两者则有所不同,泥沙扩散系数出现最大值的垂向位置要高于水流湍动扩散系数出现最大值的垂向位置；但在远离壁面的范围内,泥沙扩散系数与水流湍动扩散系数基本一致。
(4)对床面粗糙度单一变化条件下水流运动特性进行了系统研究。粗糙度变化后,内边界层的发展、床面切应力和流速的调整与来流的雷诺数、粗糙度变化形式有关。研究成果表明：内边界层向下游发展,1)随着纵向距离的增加,内边界层厚度也逐渐增加；2)在不同来流雷诺数下,内边界层发展趋基本相同。但其沿程发展有随着雷诺数的增加而逐渐变缓的趋势；3)相比于床面由水力光滑突变到水力粗糙时,床面由水力粗糙突变到水力光滑内边界层的发展更为迅速。粗糙度突变以后,床面切应力的变化主要表现为,1)在粗糙度突变点下游,床面切应力出现突变,通过一段距离之后,达到新的平衡值；2)随着来流雷诺数的增加,床面切应力的突变值也同时增大,其恢复长度相应减小。3)相比于床面由水力粗糙突变到水力光滑时,床面由水力光滑突变到水力粗糙床面切应力的突变的更为显著,而其恢复长度要小于后者；粗糙度变化后,流速变化主要变现为：1)粗糙度突变后的流速变化向下游沿纵向距离的增加逐渐趋于平衡；2)受内边界层生长的影响,外区流速略有增加；3)床面由水力粗糙变化到水力光滑时,近底流速增加,床面由水力光滑变化到水力粗糙时,近底流速减小,前者流速变化值沿纵向更快地趋于平衡。
(5)对床面粗糙度交替变化条件下水流运动特性进行了较为系统的研究。由于床面粗糙度交替变化十分复杂,为了分析粗糙度交替变化后流动特性,本文选取了粗糙度变化区域长度和粗糙度变化形式两种影响因素。当床面粗糙度交替变化时,内边界层的发展主要表现为：1)粗糙度变化区域长度很短时,内边界层发展较为迅速,随着粗糙度变化区域长度的增加,内边界层的发展逐渐趋近于粗糙度单一变化时的趋势；2)粗糙度再次突变,在突变点以后,内边界层出现了新的增长。床面切应力变化主要表现为：1)粗糙度变化区域长度较短时,床面切应力在该区域内不会出现突变,只有当粗糙度变化区域的长度增加到某一值时(通常小于单一粗糙度突变条件下床面切应力的恢复长度),床面切应力才能在该区域达到新的平衡值；2)而且随着粗糙区域长度的增加,床面切应力的恢复长度先增加然后减小逐渐趋于粗糙度单一变化时床面切应力的恢复长度；3)相比于床面由水力光滑到水力过渡再到水力光滑,床面由水力光滑到水力粗糙再到水力光滑的床面切应力突变值较大,而其恢复长度较短；4)相比于床面由水力光滑到水力过渡再到水力粗糙,床面由水力粗糙到水力光滑再到水力粗糙时,床面切应力的突变值较大,而两者的恢复长度基本一致。
(6)对床面粗糙度交替变化与河床高程高程调整共同作用下的水流运动进行了初步探讨。当河床发生淤积时,同时伴随有床沙组成发生细化,床面高程有所抬高；当床沙发生冲刷时,同时伴随有床沙组成发生粗化,床面高程有所降低。在床面粗糙度交替变化与河床高程调整共同作用时,水流运动受床面高程调整的影响为主。
The physical movements in the natural riverway, the hydraulic and hydro-power and shipping engineering are all turbulent flows under complex boundary. Such as: flow on the sand wave riverbed in the riverway, flow on the rough riverbed surface, flow around sand bars, and flow on the riverbed covered by vegetation, etc. in which the complex boundaries of flow on the sand wave riverbed and the flow on the rough riverbed surface especially on the riverbed with changeable roughness exist very widely. It significantly changes the structure of water flow movement near the bottom, and then plays important roles in discharge capacity of the riverway, bed-load transport salad change, suspended load transport and the adjustment of bed surface shape. This paper selects the two typical complex boundaries of sand wave riverbed and riverbed with changeable roughness, analyzes the characteristics of the water flow movement, further deepens the understanding of typical flow on the complex boundaries, and provides the reliable technical base for the planning, design and construction of hydraulic and hydro-power engineering and shipping engineering, etc. The main conclusions of this paper are as follows:
(1) Numerical model of flow movement on the complex boundary in the riverway has been established. The Reynolds stress model is adopted to close the flow control equation. In the numerical model, unified wall functions are adopted to reflect the impact of sands forming the boundary of the riverbed on the water flow movement. In the calculation of water flow movement on the sand wave, relative roughness, ripple steepness and relative wave height are chosen to reflect the geometric characteristics of sand wave. In the calculation of flow movement on the bed surface with changeable roughness, different roughnesses are adopted to describe the changes of roughness of bed surface. Validation calculation showed that the experimental values of the mean velocity on the sand wave bed and the mean shear stress are basically same to the calculated values, which means this model precisely described the major characteristics of the flow movement on sand wave bed.
(2) A systematic study was made of the ripple resistance coefficient and the sand-grain resistance coefficient. The sand-grain resistance on sand wave bed is surface resistance, whose coefficient is correlated to Reynolds, relative roughness and ripple steepness, and the coefficient is larger than the sand-grain resistance coefficient under the same conditions. Sand wave resistance on the sand wave riverbed belongs to physical resistance; ripple resistance coefficient on sand wave bed is closely correlated to relative height and steepness of ripples. Given the same wave height of ripples, the ripple resistance coefficient rises with the increment of sand wave steepness. In calculation of flow movement on the ripple, the wavy wall function was introduced to reflect the impact of sand gain roughness upon the flow. When the steepness of ripples is less than 0.07, the bed resistance is mainly in form of sand-grain resistance; if the steepness of ripples is more than 0.07, the bed resistance is mainly in form of ripple resistance. Increase in ripple steepness results in greater sand-grain resistance.
(3) A comparison was made between the turbulent diffusion coefficient and the sediment diffusion coefficient. On a flat bed, the sediment diffusion coefficient and the turbulent diffusion coefficient on vertical distribution are almost identical, while different on the sand wave bed; and the vertical position where sediment diffusion coefficient reaches the maximum is higher than that of turbulent diffusion coefficient; but when far away from the wave wall, the sediment diffusion coefficient is basically the same as the turbulent diffusion coefficient.
(4) A systematic study was made of the flow characteristics on the bed under uniform roughness, to conclude that after change in roughness, there was correlation between development in inner boundary, adjustment in bed shear stress and flow velocity to the change in inlet flow Reynolds and in roughness. The study concluded that the inner boundary developed toward the downstream.1) Gradual increase in thickness of the inner boundary was followed by increase in vertical distance; 2) For different inlet flow Reynolds, the inner boundary developed in almost the same trend, but development along the bed tended to slow down with increment in Reynolds; 3) In case of sudden bed change from the hydraulic rough zone to the hydraulic smooth zone, the inner boundary developed much more swiftly. Sudden change in roughness results in such change in the bed shear stress as that 1) in downstream of the sudden change point of the bed roughness, there was sudden change in the bed shear stress until new balance was achieved after flow for a certain distance; 2) as the increment in the inlet flow Reynolds, sudden changed value of the bed shear stress was increased, and the recovery length correspondingly reduced.3) In case of abrupt bed change from the hydraulic smooth zone to the hydraulic rough zone, there was more noticeable sudden change in the bed shear stress and shorter recovery length for the shear stress. Change in roughness was followed by such main change in flow velocity as 1) for different values of the inlet flow Reynolds, flow velocity change caused by abrupt roughness change was distributed along the vertical bed, until to achieve balance in the downstream; 2) there was slight increment in outer boundary caused by development of inner boundary; 3) In case of sudden bed change from the hydraulic rough zone to hydraulic smooth zones, there was increment in flow velocity of underneath part close to the bed (in which case the flow velocity value is more rapidly balanced vertically along the bed); otherwise when the bed abruptly changes from the hydraulic smooth zone to the hydraulic rough zone, there was decrease in flow velocity of underneath part close to the bed.
(5) A relatively systematic study was made of the flow characteristics in case of successive change in bed roughness. Since there was complex successive change in bed roughness, for the sake of analysis of the flow characteristics after successive change in bed roughness, two factors were taken into consideration, namely the roughness change zone length and the roughness change forms. In case of successive change in bed roughness, there was such change in inner boundary in such forms as 1) in case of short roughness change zone length, the inner boundary developed swiftly. Increase in the roughness change zone length caused the inner boundary to develop in the same orientation as in case of the uniform roughness change; 2) after the second sudden change point of roughness, there was new development in the inner boundary. The bed shear stress changed in such major ways as 1) in case of relatively short roughness change zone length, there was no sudden change in the bed shear stress; only when the roughness change zone length increased to a certain point (such a length is usually shorter than the recovery length of the bed shear stress in case of uniform roughness abrupt change), would the bed shear stress achieve fresh balance in the zone concerned.2) With increase in roughness change zone length, the recovery length of the bed shear stress would be lengthened first and then reduced until to reach the recovery length of the bed shear stress in case of uniform roughness abrupt change.3) Compared with bed change from the hydraulic smooth zone to the hydraulic transition zone and then to the hydraulic smooth zone again, there was larger sudden change in the bed shear stress value but shorter recovery length in case of bed change from the hydraulic smooth zone to the hydraulic rough zone and then to the hydraulic smooth zone again; In case of bed change from the hydraulic smooth zone to the hydraulic transition zone and then to the rough zone, or in case of bed change from the hydraulic rough zone to the hydraulic smooth zone and then to the rough zone again, there was relatively limited change in the bed shear stress and recovery length.
(6) Tentative analysis was made of the flow movement caused by combined action of the bed elevation change and bed roughness change. In case of coarsening bed sand, there would be corresponding decrease in bed elevation; otherwise when the bed sand is under refinery, there would be corresponding increase in bed elevation. Under combined action of the bed elevation change and bed roughness change, the flow was mainly under impact from the bed elevation change.
引文
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